{
  "id": "2201.10872",
  "version": "v1",
  "published": "2022-01-26T11:06:47.000Z",
  "updated": "2022-01-26T11:06:47.000Z",
  "title": "A Data-Driven Surrogate Modeling Approach for Time-Dependent Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and Manifold Interpolation",
  "authors": [
    "Martin W. Hess",
    "Annalisa Quaini",
    "Gianluigi Rozza"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "This work introduces a novel approach for data-driven model reduction of time-dependent parametric partial differential equations. Using a multi-step procedure consisting of proper orthogonal decomposition, dynamic mode decomposition and manifold interpolation, the proposed approach allows to accurately recover field solutions from a few large-scale simulations. Numerical experiments for the Rayleigh-B\\'{e}nard cavity problem show the effectiveness of such multi-step procedure in two parametric regimes, i.e.~medium and high Grashof number. The latter regime is particularly challenging as it nears the onset of turbulent and chaotic behaviour. A major advantage of the proposed method in the context of time-periodic solutions is the ability to recover frequencies that are not present in the sampled data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-26T11:06:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic mode decomposition",
      "data-driven surrogate modeling approach",
      "time-dependent incompressible navier-stokes equations",
      "manifold interpolation",
      "parametric partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}